Optimal opportunistic indirect grouping of preventive replacements in multicomponent systems

• Complex systems requiring periodic replacement of major components are studied.
• Opportunistic replacements are needed for these economically dependent components.
• We present a new tree formulation of this opportunistic indirect grouping problem.
• An efficient depth-first shortest path algorithm in Python is proposed.
• Numerical experiments show that substantial savings are achieved.

For complex systems operating in critical environments, original equipment manufacturers, operators and/or regulators often specify replacement intervals for major components before failure can occur. The fixed costs to teardown the overall system can be an important constituent of the total costs. Thus, when a preventive maintenance is scheduled to replace a given component, it may well be desirable to replace one or more other components that are within their replacement window (interval), so as to avoid repeating the teardown costs in a short while. This paper presents a novel network tree formulation of this opportunistic indirect grouping of periodic events problem. We show that, given a fixed time horizon and a moderately large number of major components, the replacement optimization problem can be represented as a tree of possible replacement combinations. Although these trees can become enormous, we have developed a Python implementation of a depth-first shortest path algorithm that can be very effective because many of the nodes of this tree do not need to be examined. Even when several million nodes need to be examined, only a few of them, typically a few hundreds, need to be maintained in memory at any one time. For larger number of components and longer time horizons, the trees can still become so large that it is impossible to examine it completely. In this case, the depth first search still rapidly finds a sequence of improving solutions and can be a very good heuristic for the problem.